Sliding mode control (SMC) is recognized as a robust controller with fast dynamic response and high stability in a wide range of operating conditions, and therefore it is widely used in the control of inverter. The sliding mode controlled inverter is in nature a nonlinear controlled time-varying nonlinear system, and it has complicated nonlinear behaviors in practice. In this paper the sliding mode controlled first-order H-bridge inverter based on pulse width modulation is taken for example. First, through observation of the waveforms under different SMC parameters, a new type of bifurcation is discovered for the first time, in which diverse multi-period bifurcations exist at the same time. Second, the discrete time iterative model is established for the system and the folded diagram is employed to observe the waveforms. These analyses of current waveforms prove that the new type of bifurcation proposed in this paper is not a route to chaos. Moreover, the stability of the system is much concerned in engineering applications. However, because of the nonlinear characteristics of sliding mode controller, the method using eigenvalues of Jacobian matrix and other analytical methods are unsuitable for the system, and the graphic methods are not accurate enough. Finally, a criterion of fast-scale stability which can accurately distinguish the stability of the system is proposed, and it can be used to provide reliable reference for the parameter design of sliding mode controller.